Exploring Novel Surface Representations via an Experimental Ray-Tracer in CGA

Conformal Geometric Algebra (CGA) provides a unified representation of both geometric primitives and conformal transformations, and as such holds significant promise in the field of computer graphics. In this paper we implement a simple ray tracer in CGA with a Blinn–Phong lighting model, before putting it to use to examine ray intersections with surfaces generated from the direct interpolation of geometric primitives. General surfaces formed from these interpolations are rendered using analytic normals. In addition, special cases of point-pair interpolation, which might find use in graphics applications, are described and rendered. A closed form expression is found for the derivative of the square root of a scalar plus 4-vector element with respect to a scalar parameter. This square root derivative is used to construct an expression for the derivative of a pure-grade multivector projected to the blade manifold. The blade manifold projection provides an analytical method for finding the normal line to the interpolated surfaces and its use is shown in lighting calculations for the ray tracer and in generating vertex normals for exporting the evolved surfaces as polygonal meshes.

Efficiency Optimization of Capsule Network Model Based on Vector Element

Currently, Deep Learning and Convolutional Neural Network (CNN) have been widely used in many fields and have generated very high value in these fields, especially in the field of image recognition. But there are some deficiencies in certain issues of image recognition. For example, CNN’s recognizing performance is not good at different angles of objects and overlapping objects. Also, CNN is sometimes very sensitive to slight perturbations, modifying one pixel of a recognized image may cause recognition errors. For these problems, the capsule network (CapsNet) proposed by Geoffrey Hinton can solve the problems of traditional convolutional networks. Shortly after CapsNet was proposed, the model structure was relatively simple, and many aspects could be explored for improvement. This paper will optimize CapsNet from two aspects: “optimization of routing mechanism” and “increase Dropout operation.” And carry out experiments and results analysis on these optimizations.

A novel method for SIFT features matching based on feature dimension matching degree

We proposes a method for fast matching SIFT feature points based on SIFT feature descriptor vector element matching. First, we discretize each dimensional feature element into an array address based on a fixed threshold value and store the corresponding feature point labels in an address. If the same dimensional feature element of the descriptor vector has the same discrete value, their feature point labels may fall into the same address. Secondly, we search the mapping address of the feature descriptor vector element to obtain the matching state of the corresponding dimensions of the feature descriptor vector, thus obtaining the number of dimensions matching between feature points and feature dimension matching degree. Then we use the feature dimension matching degree to obtain the suspect matching feature points. Finally we use the Euclidean distance to eliminate the mismatching feature points to obtain accurate matching feature point pairs. The method is essentially a high-dimensional feature vector matching method based on local feature vector element matching. Experimental results show that the new algorithm can guarantee the number of matching SIFT feature points and their matching accuracy and that its running time is similar to that of HKMT, RKDT and LSH algorithms

Sobre um experimento na educação de jovens e adultos: a aprendizagem por meio da construção de fotonovela

Resumo: O presente trabalho versa sobre o planejamento e execução de uma prática pedagógica envolvendo ludicidade na Educação de Jovens e Adultos (EJA). Via de regra, a ludicidade está relacionada com a educação de crianças. O estudo problematiza tal relação, ao pontuar o lúdico como elemento vetorial na aprendizagem e constituição do sujeito, independente da faixa etária. Dentre as experiências realizadas em uma escola da rede municipal de Porto Alegre, a construção da fotonovela intitulada “Maria Esperança” oportunizou utilizar a ludicidade como princípio orientador. A partir das análises e reflexões sobre o projeto pretende-se contribuir no debate educacional que envolve a EJA e suas consequências na formação dos estudantes. Com a pesquisa foi possível inferir que realizar atividades lúdicas com turmas de EJA, sem recair na infantilização torna-se um recurso a ser utilizado em sala de aula, desde que se considere o contexto no qual está inserido o estudante, suas potencialidades e subjetividades. Palavras-chave: Aprendizagem. Educação de Jovens e Adultos. Metodologias de Ensino. Lúdico. ON AN EXPERIMENT IN YOUTH AND ADULT EDUCATION: THROUGH LEARNING PHOTO SOAP OPERA CONSTRUCTION Abstract: This paper deals with the planning and execution of a pedagogic practice involving playfulness in the Youth and Adult Education (EJA). As a rule, the playfulness is related to the education of children. The study discusses this relationship by pointing playful as a vector element in learning and constitution of the subject, regardless of age. Among the experiments in a municipal school in Porto Alegre, the construction of photo soap opera entitled "Mary Hope" provided an opportunity to use playfulness as a guiding principle. Based on the analysis and reflections about the project, there is the intention to contribute to the educational debate involving the EJA and its consequences in the training of students. Through this research it was possible to infer that performing fun activities with adult education classes, without falling into infantilization becomes a resource to be used in the classroom, since it considers the context in which the student is inserted, their potential and subjectivities. Keywords: Learning. Youth and Adult Education. Teaching methodologies. Playful.

A Domain Decomposition Method for Hybrid Shell Vector Element with Boundary Integral Method

For the conducting body coated with thin-layer material, plenty of fine meshes are required in general. In this paper, shell vector element (SVE) is used for modeling of thin coating dielectric. Further, a domain decomposition (DD) method for hybrid shell vector element method boundary integral (SVE-BI) is proposed for analysis of electromagnetic problem of multiple three-dimensional thin-coating objects. By this method, the whole computational domains are divided into sub-SVE domains and boundary element domains. With shell element, not only the unknowns are far less than the one by traditional vector element method, but only surface integral is required. The DDM framework used for hybrid SVE-BI also enhances the computational efficiency of solving scattering from multiple coating objects greatly. Finally, several numerical examples are presented to prove the accuracy and efficiency of this DDM-SVE-BI method.

Solving Scattering from Conducting Body Coated by Thin-Layer Material by Hybrid Shell Vector Element with Boundary Integral Method

The finite element boundary integral (FEM-BI) method is widely used in the scattering and radiating problems. But for the conducting body coated by thin-layer material, plenty of fine meshes are required to discretize the geometry in the traditional FEM. It requires very expensive storage and CPU time. In this paper, the hybrid shell vector element with the boundary integral method is used to expedite the solution of thin coating problems. The shell vector elements are used to discretize thin-layer material instead of traditional tetrahedral elements. Consequently, the volume integral can be simplified into surface integral. This method reduces the number of unknowns greatly and is also extended into the complicated case of multi-thin-layer coating materials. Several numerical results are presented to prove the accuracy and efficiency of this present method.